Well, I can't speak for 4E since I never played it, and my 3E exposure was less than 1 year a long time ago.
But, 1E monsters used a chart for attacks, just like PCs did, and stat blocks were entirely different. Then, it was a case of "we designed it" that way, plus they didn't have ability scores, so their damage was also just decided it should be what it was.
In 2E, monsters also used THAC0, and their stat blocks were pretty similar to 1E.
However, in 5E, it is a case that proficiency bonus and ability modifiers determine attacks, saves, etc., just like PCs. Again, that being said, hand-waving is fine but that isn't the case. I mean, seriously, how few monsters have attacks listed they are not proficient in??
Basically the designers wanted it both ways: you basically follow the rules, but also hand-wave whatever you want and don't worry about giving any explanation or justification.